Apple has released official version of iOS 10.3.1 for the iPhone, iPad, and iPod touch which includes bug fixes, security improvements and brings support for 32 bit devices like iPhone 5-5C.
It’s a really simple and different method to install iOS 10.3.1 firmware on iPhone, iPad and iPod touch via iTunes and through OTA(Over The Air) software update.
If your device is jailbroken then the steps mentioned above does not apply. So you need to install directly or manually from iTunes as follows;
Note that restore means clean iOS 10.3.1 update and update means just moving from previous iOS version to iOS 10.3.1 update with no changes in your data.
After that select the downloaded .ipsw file of iOS 10.3.1 and you’re done. The restoring process takes a while so don’t panic. After rebooting several times that your device will be loaded with the latest iOS 10.3.1 software version.